cheesemonkey wonders

cheesemonkey wonders

Saturday, July 22, 2017

"You are what you seek," the wise one said.

Once upon a time, some time late in 2011, there were some lonely, kooky, determined math teachers trying to get better.

They searched blogs and joined Twitter in their quests, and eventually they found some like-minded spirits on the internets who were also questing.

In 2012, forty of us decided to meet in person in St. Louis and hold our own conference. Nobody outside that first group (besides Fawn, who hosted #TwitterJealousyCamp) knew or much cared about what we were doing. We were doing it because we wanted to do it. Period.

FUN FACT: Out of forty attendees at the first TMC, I was the one and only attendee from California. In fact, we had more attendees from Mississippi than from California.

It wasn't perfect, but it was real — and that kindled a spark. What made it magical was the fact that people showed up and brought their A game. I learned something amazing from every single person at that conference.

So if you attending TMC for the first time this year, please temper your freaking out with the knowledge that we started this thing because we were looking for YOU. We are STILL looking for you.

Before TMC, I always think of one of my favorite quotes from the great Jungian psychoanalyst and storyteller Clarissa Pinkola Estes:
  Even though there are negative aspects to it, the wild psyche can endure exile. It makes us yearn that much more to free our own true nature and causes us to long for a culture that goes with it. Even this yearning, this longing makes a person go on. It makes a [person] go on looking, and if she cannot find the culture that encourages her, then she usually decides to construct it herself. And that is good, for if she builds it, others who have been looking for a long time will mysteriously arrive one day enthusiastically proclaiming that they have been looking for this all along.

Friday, July 21, 2017

#TMC17 MORNING SESSION OVERVIEW: Differentiating CCSS Algebra 1 — from drab to fab using Exeter Math 1 & Exploratory Talk


How can we use a problem-based throughline such as Exeter to transform a lifeless but mandated Algebra 1 course into a rich, differentiated experience of mathematical sense-making for a wide range of students?

This morning session will be a master class in differentiating a generic Algebra 1 course using problem-based learning, exploratory talk, PCMI-style differentiation, and deliberate practice in its appropriate place together with metacognitive self-monitoring.

Over the course of our time together, we will move back and forth between the perspective of learners and the perspective of teachers. During reflective "master class" segments, we will explore the theories, techniques, and practical aspects of rearchitecting Algebra 1. During immersive “math-doingsegments, we will do selected sequences of problem-based mathematics together in groups so we can experience different approaches to concept development, cultivating habits of mind, building norms through math content, and engaging the whole student through experiential problems. Immersive segments will be interwoven with reflective, “master class” segments in which we will analyze the theories, techniques, and ideas we're exploring.

Here is the 30,000-foot overview of the topics we'll be digging into over our three days.

DAY 1 TOPICS

I. THEORETICAL FRAMEWORK:
Brief review of the How People Learn (HPL) learning cycle so that we will have a shared vocabulary for our work together. EQ: What research research informs these ideas about teaching and learning with understanding?
II. TIPS ON PRACTICAL PREPARATION FOR TEACHING EXETER:
Practical strategies and tips for organizing and managing your own teaching and learning of Exeter sequences to support your work with students.  EQ: This feels overwhelming— how can I set myself up for success?
III. REIMAGINING ALGEBRA 1 AS A COURSE IN ADVANCED PROPORTIONAL REASONING:
Why and how Algebra 1 must be reimagined as a course in advanced proportional reasoning. 
IV. EXETER'S BEST-KEPT SECRET—EXPERIENTIAL, NOT EXPERIMENTAL:
Through experiential "doing" segments and reflective discussions, we'll explore some of the ways in which the anchor problems and supporting problems within the Exeter sequences encourage students to get inside the problems in a state of flow rather than killing time filling in charts with mindless data-gathering.  EQ: How do the Exeter problems cultivate a stance of shareable curiosity?
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DAY 2 TOPICS

V.  EXPLORATORY TALK AS THE GROUND:
Strategies for integrating Talking Points as a focused technique for developing collaborative speaking and listening skills.
 VI.  RADICAL DIFFERENTIATION—THE BOWEN & DARRYL METHOD:
Structuring your room and tasks to support the needs of both katamari and speed demons. EQ: How can I create an environment that consistently values all student ideas and thinking?
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DAY 3 TOPICS

VII.   ANCHORING MATHEMATICS IN THE PRESENT MOMENT:
Anchoring students' mathematical thinking in the body, in the present moment, and in the value of their own existing knowledge and understanding.
VIII. A PLACE FOR PRACTICE ACTIVITIES:
How and where to integrate practice activities in ways that support student agency, dignity, and understanding.

Friday, July 7, 2017

Things That Work #1: Regular Vocab Quizzes in Geometry

One of the things that worked incredibly well last year—and which I want to extend this year—is regular vocab quizzes in Geometry.

Vocabulary is the gating factor for success in a problem-based, student-centered Geometry class. If you can't talk about geometry, you can't collaborate about geometry.

I learned the value of extremely routine-looking vocabulary quizzes when I taught 8th grade English with Alec MacKenzie, Linda Grady, and Kelly Starnes. At the beginning of the school year, the copy room delivered us each a giant stack of very basic matching quizzes: numbered terms in the left-hand column, lettered definitions on the right. Each student got a vocabulary workbook at the beginning of the school year. Every week we assigned a new chapter/list. Every week we gave a matching quiz. And then we would trade and grade them.

At some level, I recognize that this sounds stultifying. But at another level, it was incredibly empowering for the students. Everybody understood exactly what was being asked and expected. And everybody saw it as an opportunity to earn free points. Students gave each other encouraging written comments and cheered each other on. They saw their scores as information—not as judgment. They used what they knew to make flash cards or Quizlet stacks. They quizzed each other. They helped each other.

And nobody ever complained about the regularly scheduled vocab quiz. It was a ritual of our course.

Vocab quiz for initial unit on circles
In my first few years of teaching Geometry, I have noticed that the kids who make the effort to integrate and use the vocabulary and specialized terms tend to succeed. And the kids who don't use the language of geometry suffer. So I decided to use what I know to raise the number of kids who know and use the vocabulary by instituting regular vocabulary quizzes for the relevant lessons or chapters as we go.

Many of my discouraged math learners sprang to life when I assigned this task. They pulled out flash cards, folded sheets of binder paper in half lengthwise, and started organizing the information they wanted to integrate. In most of my classes, I noticed that the highest-status math students often seemed to get stuck while the weaker students knew EXACTLY where to start and what to do.

It was a revelation.

It also ensured that everybody spent a little quality time on the focus task of preparing for the vocab quiz on Thursday or Friday. And this, in turn, meant that everybody was a little more ready to use the correct and appropriate mathematical vocabulary in our work. They noticed more because the owned more.

Because these were "for a grade," kids put their shoulder into it. My colleagues in other departments commented about my students taking two or three available minutes during passing period to quiz each other.  It gave them hope.

Now I want to create a full set of vocab quizzes for my whole year. 

A few implementation notes:
  • I collect and shred/recycle all of the quizzes after I enter their scores so I can reuse the same quizzes from year to year. If I don't have your quiz, you can't get a score. I am strict about this.
  • Every new vocabulary term does not have to get quizzed, but lessons or units where there is a huge vocabulary burden that gets front-loaded deserves its own vocab quiz. I have been surprised to discover how many lessons are more vocabulary-intensive/language-intensive than I had realized.
  • Correct use of technical language is self-reinforcing. Once I introduce a new term, I mercilessly ask kids to remind each other of the definitions for 15 seconds in their table groups. Getting one kid to call out the correct definition to the whole class is not the point here. Getting 36 kids to all speak the definitions or the terms in their table groups is.
UPDATE: D'OH! I can't believe I forgot the most important implementation note I wanted to remind myself about!!!
  • There should be many more definitions in your right-hand list than there are terms in your left-hand list. Also definitions can be re-used. This way there isn't a zero-sum outcome if someone misses an answer.

Wednesday, May 17, 2017

Take Time to Save Time – Hall of Fame reference sheets

Inevitably, teachers get known for their mottos. Sam's mottos are justifiably world-famous. Personally, I love "Don't be a hero." Mine are known mostly around my school, but it is interesting to see how they trickle down into students' unconscious minds.

Color telling the story
Mottos pay off. My favorite is one I stole from my former colleague Alex Wilson: "Color tells the story." I don't understand how anybody can do math at a deep conceptual level without colored pencils. Color really does tell the story, especially in Geometry (see popular worked example at right).


One of my best math class mottos comes from published patterns for knitting. It is, "Take time to save time." In knitting, this means to make sure that the tension of your actual knitted work — your hands, your needles, your yarn — match the tension or gauge described in the knitting pattern. There are no shortcuts here. My knitting gauge tends to be extremely big or loose compared to most pattern-makers. I often have to use much smaller needles than specified in order to achieve a good match with the specified knitting gauge.

In my classroom, "Take time to save time" means, synthesize your learning into a reference sheet. For all tests but the final, I allow students to have and make a half-page reference sheet.  The first rule is, you can have anything you want except a photocopy of my work on your reference half-sheet. The second rule is, if you have more than a half sheet of 8.5 x 11 inch paper, then I get to tear it in half and choose which half you get. This rule gets tested even when I emphasize it. Every year somebody tests this rule. "But Dr. S! I only wrote a half-page worth of stuff on the paper!" It doesn't matter. I usually rip the whole thing lengthwise so they only get the right-hand half of the paper.

It makes its point.

In knitting, this point gets made by the scale and size of your finished object. If you insist on not checking your gauge, at some point, you will end up with a finger-puppet-sized sweater or a scarf the size of Lake Tahoe.

Clearly this student is going to ace the final.
In our classes, this point gets made by your performance on our common final exam. Students who have been practicing making clear, concise, summaries and examples of their work and key points tend to turn in consistently strong performances. So on the final, I allow a full-page reference sheet (both sides). I emphatically want students to consolidate their understanding and create their own examples. That is where the learning happens.

So I was thrilled today when I asked to see examples of in-progress reference sheets. Many of them made my Hall Of Fame request to scan for posterity. This Algebra 1 student has totally nailed her understanding of mixture problems. This is the best example I've seen of a student consolidating her understanding of these modeling challenges.


Thursday, December 1, 2016

The Festival of Reassessment (SBG)

December is when I am truly grateful for strong routines. They mean I can split the class up and still count on everything moving forward. I am running behind in my pacing, so I needed to set up a mass SBG reassessment opportunity for slope skills yesterday. I set up all the reassessors along the window side of the classroom and all of the non-reassessors on the hallway side of the room. The non-reassessors worked on linear systems skills and problem-based learning while the reassessors worked on demonstrating mastery of slope skills.

Whenever a reassessing student finished their work, they brought it up to be rechecked. I went through it right then and there while they watched. “Uh huh... uh huh... uh huh...” until “Oh noooooo! Why is this negative?!?!? It ruins everything! Go back and fix it!!!” And then the next student moved forward in the queue.

We went through this process of working and my checking and sending kids back for about 40 minutes. “Nooooo!!!” I would circle something and pretend to freak out, sending them back to fix stuff. It became a carnival. “AAACK!" I would say. "Go back and fix this!” Seeing this happen in real-time changed kids’ relationships with their misconceptions. It reminded me of piano practice as a child. Something would splatter in the midst of a phrase or figure and I would have to go back to the beginning, willing the figure to come out right through my fingers on the keyboard.

We kept going until all 12 students had triumphed over slope and point-slope form. What I loved about this process was how it transformed the social focus of the process of understanding to us (the whole class) against the skills. Kids were going wild and cheering when somebody finally triumphed over the "slope and point-slope” process, jumping up and down and hugging their newly non-reassessing classmates and friends.

The goal became one of getting everybody in the classroom over the finish line. From individual mastery to collective. Students stopped focusing on who had status in the classroom and who did not. They stopped thinking about their place in the social hierarchy and instead lost themselves in the flow of doing this f***ing slope and linear equation problem.

And then as each new classmate finally triumphed over the skill, the whole class felt truly victorious.

Everybody got the individualized attention they needed as they drove their skills forward, and we also bonded as a collective community, advancing our work as a group.

In these divisive times, I think this might be an important process to cultivate.

Tuesday, November 22, 2016

Blogs feed my teaching soul, but Twitter helps me feel less alone

As I've been working on my National Board certification, I have come to appreciate something that the #MTBoS gives to me every single hour of every single day.

My tweeps' teaching blogs feed my teaching soul. Seriously, any time I feel stuck, I can just fire off a search in the MTBoS search engine and BOOM, I get drenched in a downpour of borrowed genius.

But in the moment, when I am freaking out or feeling lost, Twitter makes me feel ever so much less alone.

So thank you, my tweeps, and keep going. I am thankful for you Every. Single. Day.

Sunday, October 23, 2016

Graphing Stories Meets Estimation 180: A Love Story

On Friday we started our Functions unit, and as always, my go-to is to start with Dan Meyer's Graphing Stories.

After they pick up a Graphing Stories worksheet, I give them a brief set-up, explain that the guy in the video is my friend Dr. Meyer (though now I have to explain that this was a long time ago, in a galaxy far, far away, when he was a young Jedi-in-training), and promise them that I will rewind the videos as many times as they want, to whatever point they want, for as long as they want, so we can figure out as closely as possible what their graphs ought to look like.
screen shot of Dan leaning over the railing of the footbridge
Portrait of the artist as a young Jedi warrior
Only this time, we encountered a spontaneous twist.

The first video went off without a hitch. Using QuickTime, I have an action-only version of the first 15-second video (Dan walks over a bridge in a Santa Cruz park), so that it doesn't accidentally reveal anything I'm not ready to reveal yet.

I explained that my friend Dr. Meyer is unusually tall (I gave his actual height, which can be found on his web site) and this gave students the idea to "measure" him onscreen so they could try to better estimate the rise of the bridge.

This gave me an idea.

The second video in the series is of Dan descending some exterior condo stairs, but after the first viewing, an argument broke out in the discussion as they tried to find some hook they could use to improve their estimations. "A car is, like 6 feet high!" "No, the stairs are about 5 feet in total!" Blah blah blah.

Enter Estimation 180 thinking.

My classroom is right next to the door to the stairs up to the small faculty parking lot. I pointed to two kids. "OK, you and you — take a yard stick, carefully cross the driveway, and go measure some average car heights in the teachers' parking lot."

The arguments continued so I pointed out another kid, one who was extremely interested in the stair height but who has never before piped up in class. "Pick a helper, grab a yard stick, and go out to the stairs and find an average for the stair height."

While our data gatherers performed their missions, the estimation arguments continued inside the classroom. "The car is only about 4 feet high!" "No, it's not!" "What about the lamp post—can we use that?"

Five minutes later, our intrepid explorers returned and we harvested our newfound information.

Then we continued working on the Graphings Stories task.

The funny thing was that our estimates led to wildly wrong answers, but that wasn't the most important thing. Instead, what was powerful was the level of engagement in discovery that electrified the room.

Instead of considering the need to quantify to be yet another tedious task that stood in the way of getting "the right answer," students started to lose themselves in the flow of the process of mathematizing their world.

And isn't that the whole point?

So thank you to Dan (@ddmeyer) and Andrew (@mr_stadel) for giving me the tools to slow my kids down and help them to find the wonder in everyday situations.

PS — I still haven't revealed the "answer" to Graphing Story #2 yet. But I'm curious to see what unfolds in class when we come back tomorrow. ;)